Compensation of polarization-dependent loss using noiseless amplification and attenuation

R. A. Brewster, B. T. Kirby, J. D. Franson, and M. Brodsky

Phys. Rev. A 100, 033811 – Published 11 September 2019

Abstract

Polarization-dependent loss (PDL) is a serious problem that hinders the transfer of polarization qubits through quantum networks. Recently it has been shown that the detrimental effects of PDL on qubit fidelity can be compensated for with the introduction of an additional passive PDL element that rebalances the polarization modes of the transmitted qubit. This procedure works extremely well when the output of the system is postselected on photon detection. However, in cases where the qubit might be needed for further analysis this procedure introduces unwanted vacuum terms into the state. Here we present procedures for the compensation of the effects of PDL using noiseless amplification and attenuation. Each of these techniques introduces a heralding signal into the correction procedure that significantly reduces the vacuum terms in the final state. When detector inefficiency and dark counts are included in the analysis noiseless amplification remains superior, in terms of the fidelity of the final state, to both noiseless attenuation and passive PDL compensation for detector efficiencies greater than 40%.

Received 21 May 2019

DOI:https://doi.org/10.1103/PhysRevA.100.033811

Physics Subject Headings (PhySH)

Quantum communication Quantum optics

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

R. A. Brewster¹, B. T. Kirby², J. D. Franson¹, and M. Brodsky²

¹Department of Physics, University of Maryland Baltimore County, Baltimore, Maryland 21250, USA
²United States Army Research Laboratory, Adelphi, Maryland 20783, USA

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Vol. 100, Iss. 3 — September 2019

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Images

Figure 1
Our input polarization qubit experiences unavoidable PDL modeled as shown in the first box labeled PDL. For simplicity, we consider the case where only the horizontal polarization mode was initially attenuated by a factor $t_{h}$ . Following this PDL, we correct for it using either one of two possible attenuation schemes or an amplification scheme. These schemes are further detailed in Fig. 2. In the case of a correction using attenuation shown in the upper box, we attenuate the vertical mode to balance it with the horizontal mode. Similarly, in the case of amplification shown in the lower box, we amplify the horizontal mode to balance it with the vertical mode.
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Figure 2
A more detailed description of the three possible correction schemes. In passive attenuation the input state experiences loss where the ancillary mode is lost to the environment. In noiseless attenuation [16] the same situation occurs except we instead postselect on vacuum in the ancillary mode. In noiseless amplification [17] an input state undergoes unbalanced teleportation by postselecting on the states specified at the detectors. As we will see, noiseless amplification provides for the best fidelity at the expense of the transmission rate.
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Figure 3
Plot of the acceptance rate or probability of success of each of the possible correction schemes as a function of the PDL defined in Eq. (20) in decibels. Since passive attenuation is deterministic we will always accept the output state. From this figure we see that noiseless amplification will have a smaller acceptance rate than the other compensation schemes. In the noiseless amplification considered here we only accept one possible Bell state outcome. It might be possible to improve the acceptance rate for noiseless amplification by accepting other Bell state outcomes and other techniques.
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Figure 4
Plot of the fidelity as a function of the PDL defined in Eq. (21) in decibels. As we can see, the fidelity will always be better in the case of noiseless amplification than for noiseless or passive attenuation. As mentioned in the text, this is due to the reduction in the probability amplitude of the vacuum term. This plot was generated for the ideal case of no detector noise.
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Figure 5
Model used to simulate imperfect detectors with dark counts. An input state is mixed with a thermal state $ρ_{T}$ using an unbalanced beam splitter with transmission equal to the detector efficiency $η$ . The temperature of the thermal state is chosen to be function of $η$ to guarantee a constant probability of finding a dark-count photon per time step.
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Figure 6
Plot of the fidelity in the case of imperfect detectors as a function of detector efficiency $η$ . We are modeling an imperfect detector according to the diagram in Fig. 5. This plot was generated with an initial 3 dB of PDL and a dark-count rate of $4 \times 10^{- 5}$ photons per time step. We see that in this case, noiseless amplification still does better for larger detector efficiencies. The vertical lines correspond to values for realistic detector efficiencies. The line at $20 %$ represents indium gallium arsenide (InGaAs) single-photon detectors [27] and the line at $85 %$ represents superconducting nanowire single-photon detectors (SNSPDs) [28].
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